By Nathan Tankus, a student and research assistant at the University of Ottawa. He is currently a Visiting Researcher at the Fields Institute. You can follow him on Twitter at @NathanTankus

Since Bernanke started talking about “tapering off” Quantitative Easing, the bond markets have freaked out. This is a very logical reaction.

Before last month, it seemed like QE would go on indefinitely. Once that belief was shaken – even in the slightest fashion – everyone ran to the exits. Bernanke and other Federal Reserve economists appear bewildered by this phenomenon. The impression one gets from their follow-up comments is that they wished they could ask bond speculators “did you read the damn speech?” The answer, of course, is no and for good reason.

All investors need to know is the conditions under which QE (and for that matter, the Zero Interest Rate Policy) will be pursued has changed. Now the substantive change may actually be relatively minor, but that’s irrelevant to speculators. The reason is very simple: those holding assets with longer maturities will take huge capital losses with relatively small changes in interest rates (As a reminder: it is basic “bond math” that a change in interest rates send bond prices in the reverse direction. A rise in interest rates makes bond prices fall and a fall in interest rates make bond prices rise). It is better to exit now when those future changes are uncertain then take even more massive losses.

This is the logic behind the actual “liquidity trap” presented by Keynes in the general theory. Specifically, Chapter 15 entitled “The Psychological and Business Incentives To Liquidity.” Here he argues that every fall in the interest rate relative to what is commonly believed to be a “safe” rate increases the “risk of illiquidity”. The the “risk of illiquidity” is the risk of holding an asset not easily convertible into money at “book” value (this also means an asset is more or less “liquid” based on the relative easiness to convert into money “book” value). Further, rather then seeing interest as a return to “waiting”, Keynes argues that it is “a sort of insurance premium to offset the risk of loss on capital account”.

How can one evaluate the uncertainties relative to the “insurance”? By what has been subsequently known as “Keynes’s square rule”.

The square rule was defined by Keynes in this chapter as “an amount equal to the difference between the squares of the old rate of interest and the new” (mathematically represented as Δi = i2 ). If interest rates (at that maturity) are expected to rise faster then a squaring of itself, it means your capital losses (market price of the bond or investment) will fall faster then the increase in the rate of return (and vice versa).

Based on this understanding, a liquidity trap is not a short term rate of interest at zero but a uniform expectation that interest rates will rise to such an extent that the rate of return on a bond or equity won’t preserve your principal and thus a refusal by anyone but the central bank to buy bonds at such a high price (i.e., low interest rate).

Keynes says explicitly in chapter 15 that “what matters is not the absolute level of r but the degree of its divergence from what is considered a fairly safe level of r, having regard to those calculations of probability which are being relied on” (r being the rate of interest). Why this confusion has resulted has many complex historical reasons, not least of which is economists disinterest in actually reading and comprehending what was written more then five years before them.

A normally good economist has fallen into this trap by repeating an error Irving Fisher made over 80 years ago that Keynes’s argument was explicitly a response to (see Kregel’s enlightening account, and incidentally meticulous critique of Krugman, here) . Specifically, Bruce Bartlett argued that:

Because there is so much concern right now about the economic consequences of higher interest rates, which are almost universally viewed as negative, I would like to note that higher rates will raise the income of many middle-class people who tend to keep their savings in bonds, certificates of deposit and savings accounts that yield very little return.

Irving Fisher went further then this, arguing that increases an interest rates could always compensate for inflation. Still, the basic error is the same. What Bartlett is forgetting is that if the interest rate rises too fast those “middle-class people” will take much larger losses on the value of many of their assets then they will get back in interest (he has another argument based on textbook economics that I may respond to in another post). That is without even taking into account the higher borrowing costs that many would most likely face. Remember also that at such low interests rates “too fast” is actually a very small increase. To go back to Keynes:

If, however, the rate of interest is already as low as 2 per cent., the running yield will only offset a rise in it of as little as 0.04 per cent. per annum. This, indeed, is perhaps the chief obstacle to a fall in the rate of interest to a very low level. Unless reasons are believed to exist why future experience will be very different from past experience, a long-term rate of interest of (say) 2 per cent. leaves more to fear than to hope, and offers, at the same time, a running yield which is only sufficient to offset a very small measure of fear.

The “reason” in our current situation, whether justified or not, was Quantitative Easing. It is quite reasonable for participants to panic once the hope is removed and all that is left is fear. QE was bad policy but once it was done, it could only be ended very gradually. Tapering may prove to be as ad-hoc and inadvisable as QE itself.

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50 comments

In addition to “institutional” buyers of high-yield paper, QE has enticed a lot of retail customers (many seniors who need income and don’t want to eat into capital — there’s a lot of investor psychology needing to be unpicked in that choice of assets, but that’s for an different time !) fleeing from CD type of products or sovereign debt-based vehicles.

Mr. Market has a noisy wobble at the merest hint of tapering but, to misquote Stalin, how many votes has he got ? The real political imperative has become (and the politicians are, as usual, behind the curve on this one and just now stumbling on this unintended consequence) to not have savers, especially retirees, having to eat losses.

Now, if we’re being purists here, we should really say “tough” to those people. We’d, in fairness, say the same to the TBTFs or a hedge funds. But I’d argue that this class of victim of QE didn’t have much of a choice. That’s my moral compass point in this one, though, I’d be happy for others to disagree. Regardless of what we think, however, it’s not just financiers any more — this has morphed into a retail (ordinary voting member of the population) castle in the sky.

“i would like to note that higher rates will raise the income of many middle-class people who tend to keep their savings in bonds, certificates of deposit and savings accounts that yield very little return.”

what is Bartlett smoking? (I’d always thought that he was one of the more street-wise conservatives)

Absolutely no non-1% people I know have enough money in their checking/savings person to make rising interest rates worth while.

Main non-1% asset vehicles are housing and 401k/stocks. both don’t do well in with rapidly rising rates.

and don’t forget the bottom 30-50% who living paycheck to paycheck…..or more apt overdraft to overdraft.

I think that the concept of sovereign interest rates is extraneous to a well functioning economy.. Job creation (gainfully employing labor) can lead to a sustainable economy..

“” it is important for people to recognize that any constraints on the authority to create money without issuing debt instruments that may exist in current practices are, as MMT says, self-imposed constraints.””

“”””Paradigms advance by creating cognitive dissonance in those who accept the old paradigm or who are neutral in relation to that paradigm. That is, I think, exactly what we are doing.”””

I like the above statement where paradigm shifts (big changes in the way we look at things) can be caused by cognitive dissonance (when we have to deal with conflicting thoughts)

I think MMT (modern monetary theory) fits into this category. Some people describe it as MMT for me but not for thee. Meaning that when our politically connected banks need bailouts to the tune of trillions of dollars the money is made available even though 90% of the population is against it. But when the general public needs a bailout we are suddenly short of funds.

This sort of cognitive dissonance can lead to a paradigm shift.

———

I like to view MMT as the progeny of the condor and the eagle ;). It is very rational but I think that the trouble people have with incorporating its ideas gives it a mystical quality..

“”””The Prophecy of the Condor and Eagle” is typical. It states that back in the mists of history; human societies divided and took two different paths: that of the condor (representing the heart, intuitive and mystical) and that of the eagle (representing the brain, rational and material). In the 1490s, the prophecy said, the two paths would converge and the eagle would drive the condor to the verge of extinction. Then, five hundred years later, in the 1990s, a new epoch would begin, one in which the condor and the eagle will have the opportunity to reunite and fly together in the same sky, along the same path. If the condor and eagle accept this opportunity, they will create a most remarkable offspring, unlike any ever seen before.

“The Prophecy of the Condor and Eagle” can be taken at many levels – the standard interpretation is that it foretells the sharing of indigenous knowledge with the technologies of science, the balancing of yin and yang, and the bridging of northern and southern cultures. However, most powerful is the message if offers about consciousness; it says that we have entered a time when we can benefit from the many diverse ways of seeing ourselves and the world, and that we can use these as a springboard to higher levels of awareness. As human beings, we can truly wake up and evolve into a more conscious species.””” (John Perkins from ‘Confessions of an Economic Hit Man’ 2004)

Your comment is right on the mark and all discussions of finance or politics must start with the sorts of insights you have articulated. Using all the most advanced and sophisticated intellectual tools at our disposal we cannot fail to grasp that we are totally f!cked. So what sustains us? What offers us a way forward out of the conceptual cul de sac our institutions and leaders have led us into?

I suggest that reality is much larger than we insist on admitting. I suggest that the evidence for this is overwhelming using our own intellectual tools. I suggest that our collective views on politics, culture, economics, philosophy are drastically at odds with what is demonstrably true. We are so attached to a mid 20th century view of reality that we have constructed a cargo-cult-like conceptual framework that is becoming more and more insane with each passing year.

Looks like it could be a rally call for all the people in the know with large diversified portfolios to start a SLOW unwinding in markets to maximize their profits on the exits ( sovereign wealth funds+ top 5%). The Retirees in wall st. need to worry about where to put welfare payments to keep from getting another hair cut, or the least amount of losses. But to tell you the truth I think they are just rattling sabers to make it seem like American ideals are going to return to the markets in the US. lol

If you hold a bond to maturity you get all your principal back unless it defaults. You may lose purchasing power but that will be from inflation. Or you might gain purchasing power if there’s deflation.

I bet there will still be plenty of people buying bonds as rates rise. There won’t be any liquidity trap. New investors will jump to get a piece of rising yields. And who knows? Rates might go down again if growth stalls.

I may be dense but I don’t get the squared-thing either. If rates are 3 now and they’ll go to 5, that’s 25-9 = 16. What’s 16? what unit of measure is it? It sounds like this is some sort of duration proxy but duration seems more precise.

does anything make sense about this post? Nathan what’s up dude, are you smoking weed up there or is your brain fried from reading Keynes? haha. Best just to grok reality and figrue it out by staring at it. Forget these wakcos like Keynes and Hayek and god Forbid, somebdoy like Milton Friedman. Better to check out youtube and Adele videos.

faaak here’s Adele herself. check this out Nathan and tell me if this isn’t scary. whoa! this is far scarier than anything Bernanke says, if you’re the boyfriend she’s talking about you better duck big time.

I’m glad someone else finds the logic of this odd. Ever since this Tapering story started I’ve been puzzling over why rising interest rates would cause the value of bonds to fall. And that square rule bizness would strike me as fishy if it didn’t have the authority of Keynes’ name behind it, I agree.

On the general reason that a rise in the interest rate makes bond prices fall, it is actually very simple. Remember that we are talking about EXISTING bonds and their market value not “hold to maturity” value. I will give a very stylized example but it makes the general point. If someone sells a bond for 100 dollars at 5 per cent interest (meaning it pays out 5 dollars every year) and then interest rates rise to 10 per cent, no one will pay 100 dollars for a bond that earns 5 per cent when you can buy a bond for 100 dollars that earns 10 per cent. what then happens is that the only way someone who wants to sell the bond will be able to sell it is if they offer the 10 per cent return expected at that maturity. how can a bondholder provide that? by selling the bond for less. In this example the bond would have to be sold for 50 dollars to provide a 10 per cent return (50/5 is 10).

This is why the market price for existing bonds falls when interest rates rise. Craazyman is of course right that the “hold to maturity” value doesn’t change but that is meaningless for someone who needs to sell. Even for someone who intends to hold it to maturity, it is very painful to sit around earning the old rate of interest as people in the same asset class taking the same risks are earning a much higher rate of return. it’s like picking up 5 dollar bills off the floor but not being allowed to pick up the 10 dollar bills that have started falling.

Thank you for that “NC for Dummies” version, that is more clear to me now.

BTW, I haven’t read Keynes, but I like seeing specific chapters of his cited in reference to current events. It shows how relevant he remains and is good encouragement to read him eventually.

One thing I am still unclear on, if you or others care to say: is Keynes’ rule a hard rule of how much bond values will fall, or is it a general estimate that will probably hold true? If a hard rule, is it derived as a general rule based on the sort of particular example you give above, or in some other arcane way?

It is more a rule of thumb. Remember Keynes invested all through out the 1920s and 1930s so i suspect that this is something he picked up from investing rather then something he learned by reading books. It is a rule of thumb because all it tells you is how bond prices fall or rise relative to changes in the rate of return without any change in any other relevant variable such as default risk. The point Keynes was originally making was that even in the most stylized form changing interest rates can’t compensate for the changing rate of inflation.

Nathan is correct that the value of a bond with a reasonably long time to maturity will fall if rates rise.

The mathematical concept of “duration” measures the sensitivity of a bond’s price to changes in interest rates. It’s easy to Google it and read up on it.

However, there won’t be any liquidity trap and Keynes concept of some square of the interest rate differential makes no sense. Bond investors will continue to pile in to bonds as rates rise because the economy creates new savings with long-term, risk averse funding goals that have to be invested in something appropriate. There’s several hundred years of bond market history that shows rising yields don’t squelch demand for bonds.

And it’s also correct to say the value of your individual bond will eventually be it’s full principal price at maturity provided it doesn’t default. I hate being serious in peanut gallery comments, it’s too much like work, so if anyone is interested they can read up on “duration” and the mathematics of bond returns (a riveting topic to be sure!). What was Keynes thinking? Economics never makes any sense no matter who writes about it, so it’s better just make it up for yourself as a hobby between Youtube surfing sessions. There’s several other Adele videos that are very good, like the Bond movie theme song “Skyfall” and the one where she’s walking by herself in Paris singing “Someone Like YOu”

Craazyman, it appears that you’re not making any attempt to understand what other people are saying and would prefer to argue against positions you make up.

“Bond investors will continue to pile in to bonds as rates rise because the economy creates new savings with long-term, risk averse funding goals that have to be invested in something appropriate. There’s several hundred years of bond market history that shows rising yields don’t squelch demand for bonds.”

Show me one shred of evidence that either I or Keynes said that people won’t buy bonds as interest rates rise. that has nothing to do with this post and is merely something you made up. What a liquidity trap is is the refusal to buy bonds AT THE CURRENT PRICE (ie interest rate) because of a uniform expectation that interest rates will rise in the future causing capital losses. saying that people will buy bonds at lower prices (ie higher interest rates) in response to this is like saying there is no such thing as an uncomfortable temperature because people will just enter an air conditioned building.

again you made no attempt to understand what the Square rule actually is so I feel no need to reexplain it.

OK maybe I did make it up but it was by accident! I always thought a liquidity trap was when people wouldn’t part with their money at any interest rate, or any reasonable interest rate anyway.

By the way, what is the 16? I honestly don’t get what Keynes was referring to with this interest rate differential squared stuff. 5% squared is 25 and 3% is 9, so 25-9 is 16. tHIS ISN’T a friviolus example it’s right from the Post!

I tried to understand it but couldn’t, although I admit it migfht make sense somehow that I don’t get.

How hot is Adele’s singing by the way and aren’t those lyrics just fire in words? How can anyone sit in a library reading economics when there’s Youtube?!! Faaaaak. That and beers will ruin you as a scholar.

Adele is HOT. Nice to be able to say that about a plus size beauty. Speaking of which, model Robyn Lawley caught my eye while checking Huffpo yesterday, found a story from Australian Magazine about her:

“True, she is stunning: beautiful, athletic, tall. Yet because Robyn Lawley is a size 16, she is not simply called a model; she is classified as a “plus-size model”. To which she replies, “I’m a normal size. I wish we could all be known as models, rather than ‘plus-size’. It’s skinny models who should be called ‘minus size’.”

Maybe if this trend takes off young girls can stop hating themselves and eating disorders will become less common.

Please do some reading about bonds. Interest rate risk is at least as big a worry for fixed income (bond) investors as credit risk.

If interest rates rise, it’s usually because inflation expectations have risen. At pre taper talk yields, investors in long dated bonds were guaranteed to lose relative to inflation. The Fed deliberately created negative real yields.

All investment portfolios are marked to market. Why in God’s name should anyone treat bonds differently than stocks?

And most retail investors don’t hold bonds individually, they hold bond funds which are traded and their fund reports what amounts to the current yield (there’s a term of art, like one-month yield, which I believe is the yield the fund has averaged over the most recent month).

Look, Pimco’s flagship bond fund lost something like 1.9% in May. This is a really basic concept, time value of money and the “time value” is not static, it depends on prevailing interest rates.

Yes, most retail investors (like me), buy and hold to maturity. In this case, you’ll only lose principal through inflation and default.

OTOH, you’ll see the daily value of your account drop. If you hold long term bonds, you’ll see it drop a lot. For conservative investors, this is hard to watch.

BTW, I don’t always hold to maturity. At around the 2 year mark, it often makes sense to sell a now low yielding bond and buy a longer duration higher yielding bond for my ladder. This may make sense even if I take losses.

A large percentage of investors don’t even realize bond prices drop with an increase in rates. Even more don’t even realize there are credit spreads so even if rates don’t go up that much credit spreads could soar.

Once riskophobic investors who picked bonds for an extra 1% realize this, it will interesting to see where they decide to park their money, if there is any left.

Also, let’s not forget all those investors who bought dividend stocks as bond replacements…

1. Most retail investors do NOT “hold bonds to maturity”. They are in bond funds or balanced funds. If you buy a corporate or Treasury bond in retail denominations you are asking to be raped on the price. And some hold those funds in 401 (k)s or IRA. The big exception would be muni bonds (those are are a retail product) and it’s more common for investors to buy them individually (although there are also muni bond funds).

2. Retail investors get monthly statements from their broker. Plus they can view their accounts on line. Those are marked to market. They’s see huge losses on bonds and bond funds when they get their June statements. I don’t know about other brokers but at Vanguard (and I mean Vanguard brokerage, they do have a brokerage operation in addition to their funds) you can’t even see the original cost basis in your normal reports, nor can you readily obtain it from them.

Yes, I would guess people investing in bond funds (which are most people) will freak out when they see the losses.

My mistake. I should have said most of the ‘retail’ investors buying bonds outside of funds hold to maturity. This is a small subset of all retail investors, almost all of them private banking clients.

Pricing (and price discovery) has gotten a lot better over the past 5-10 years. $25 to participate in Treasury auctions. You can go to Treasury Direct route for free… but $25 is a small fee on a $100,000 bond.

Still, pricing is a huge issue, which is why I hold a lot of bonds to maturity. You only trade once. This is especially true with munis which are not as liquid and are much more costly to sell.

what you’re missing is that we’re talking about assets that (generally) have a medium to long maturity. the losses in market value of a bond or other security might not seem important to you but I promise you that they matter a lot to those who are holding these assets. If someone is going to retire soon and wants to cash out, the fact that the market value of their assets took a tremendous dive will have very real, material effects.

none of this has anything to do with whether or not people will buy bonds at higher interest rates. that point makes no sense relative to this piece. interest rates rising means that the price of bonds fall in concord. this is about the people who are already “locked in”.

your calculation is wrong based on the example (this is why it’s important to follow the links… two of the three give numerical example). In your example the change in the interest rate is 0.02 (2 per cent ie 5-3) and the interest rate squared of itself is 0.009 (9/10 per cent) so that the interest rate rise will create more capital losses (at that maturity level) then the investor gets back in higher interest. if the rise in interest rates stops after that year they will then start getting a higher return without further capital losses. but it does have important effects now even if they eventually earn more.

OK, so the decimal goes in front! I’ll check that out and recalculate. We;ll 0.9% is not a lot to have to make up other ways.

bond managers can make money by trading on credit spread volatility and buying improving credits and making capital gains from spread compression, even if rates are rising, so it’s not a guaranteed fail.

Guys like Keynes and other library theorists always make things simpler than they really are.

“Make things as simple as possible, but not simpler” is what Einstein supposedly said to young physicists.

remember he was an actual trader so this probably didn’t come from reading books at all but being a participant.

you’re correct that this can be counterbalanced by taking an opposite risk and not being net long but that isn’t really relevant to the initial point. I think Keynes had a real knack for making it as simple as possible but no simpler. Remember he admired Einstein and named his book The General Theory. not a coincidence.

p.s. I absolutely love when someone reassesses after an initial reaction. it takes real intellectual honesty to do that.

Why would somebody who is going to retire soon invest in assets that have a long maturity with a low rate? I doubt if the average retail investor considers short term bond investing a good vehicle for retirement assets.

why would someone invest in a collateralized debt obligation or any other financial product that will blow up in their face? why would municipalities and homeowners take on interest rate risk for a slightly higher return (promised or real) now? I think you overestimate the average investor and the financial incentives that agents of the average investor have.

I’m confused. Are you suggesting we are forced to keep rates low forever because of stupidity of some investors, moral hazard be damned? Seems like a convenient excuse for financiers who game the system while pointing at the perils in store for these poor innocents.

QE/ZIRP was not done for its own sake. It was meant to remedy something else. Now, QE/ZIRPis supporting artificial stock and bond market prices that keep public retirement systems and private definded benefit pension funds from looking even more underfunded than they already do. And the GASB is proposing pension accounting changes that could threaten Los Angeles (and a few more California cities) with municipal bankruptcy even if the stock and bond market prices don’t fall significanlty. If those prices do fall significantly, the ride could get very bumpy.

Is there a medical analogy to the QE/ZIRP remedy? Maybe it’s analogous to controlling heroin addiction by hooking the patient on methadone–one can’t reasonably expect to taper an addict off of methadone, no matter graudally one proposes to do it.

Got a link or any kind of source reference for those proposed GASB changes (and associated analysis of same)? I live in CA and have watched the unfunded pension liabilities issue unfold like one long, never-ending slow motion train wreck.

The cities can’t honestly continue to project fund returns (or discount future obligations) at 7.75% in a ZIRP environment. But if rates go up due to the end of ZIRP, the increasing discount of currently funded assests will make their current funding status even worse.

For a medical analogy I think cyanide poisoning might work. The patient is slowly being poisoned with cyanide (the various forms of fraud from ninja loans to servicer abuses to corporate governance problems etc) and is being treated with high doses of caffeine (QE) which produces a temporary high but comes with its own problems. The patient needs to have the cyanide removed and instead of caffeine needs a nutritional balanced diet.

(I consider this an MMT type re-distributional approach rather than an austerian take your medicine approach)

Here is a thought experiment for folks to consider – if you were expecting a big rise in interest rates one day and didn’t want to trust the stock market you could park money in something like Vanguard’s Short-Term US Treasury Fund (VFISX). The maturity of the bonds held by it go from 1 to 4 years and its a good company with low fees and just wait the mess out. You would lose some yield but you would protect your capital. Now Vanguard also has other versions of the fund that are Intermediate-Term (VFITX) and Long-Term (VUSTX). To see what happened to each you can just go to your favorite charting site and cart all 3 against each other. It is almost a text book image of what you would expect.

That is actually not good advice and please don’t give financial advice here.

Vanguard short duration funds (all 2-3 year duration) have still suffered meaningful losses in May and June.

If you are in bonds during a tightening cycle you will take losses. Telling someone to step in front of that and get in short term funds is just telling them to lose money but how to lose less money than if they went longer maturity.

Unfortunately I am like many of the unwashed who are trying to preserve capital in a world where all the forces out there know more than we do. The comparison of the 3 funds was added since it supports the author’s point as the graph demonstrates the range of volitilities that exist among the three classes of bonds with the longest term being the most volitle and how all 3 are now falling, be at very different rates, as we approach a possible tightening period.

My interpretation of this could be 100% wrong as my training in economics is limited to one class as an undergraduate. Again, I can assure you I am not interested in advising anybody but rather trying to understand an archane issue to hopefully prevent future mistakes. Re: the politics of the situation – I am quite sure none of the QE has been or is being done in my interest, rather I am just along for the ride like the rest of the folks out there. Clearly QE, the money printing and bond buying has massively distorted the economy and will make any future recover more painful for all.

Did investors really think that? At no point did the Fed say it would. They were often vague about when it would end, but not that it would eventually end. I mean, you know, a thing that can’t go on forever, won’t. If the bond investors failed to take that into account, then that is just stupid.

No, the panic was out of ignorance, not some deep understanding of Keynes. That it was ignorance will be borne out by people piling back on after the Fed Board has repeatedly restated what was always obvious.

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